Uh, the whole Liu story was confusing and well...didn't make sense
First off that's kidnapping, so Gotham sponsors that. Diplomatic immunity? What was China's response to this because technically they are KIDNAPPING a Chinese nationalist. I don't know about you but there has to be political and military ramifications on this. The United States isn't going to go, oh well, suck it China. We captured one of your guys. And how did they even accept this?
He'd only have diplomatic immunity if he was diplomat. It's likely as businessman no such shield was held over him.
And we've really no idea how it was "explained" to China what happened how Liu got back to Gotham. The US/Gotham could've just played a "we don't know how he got here but now that he is we're keeping him" card. We've no idea what the world-politics are like in this universe.
That's exactly what did happen. That's why Dent said something like "We don't know anything about Liu's travel plans, we're just glad he's back." And Gotham
didn't "sponsor" a kidnapping, because Batman was a vigilante acting on his own, as far as the rest of the world knew. Only Dent and Gordon knew the truth. Gotham PD even had an official policy of arresting Batman on site (which they weren't going to enforce, but still, to the rest of the world, that meant they were not working with Batman).
I just don't get why they had to pin the murders on Batman, or on anyone at all, even the Joker. They could've just left them as more unsolved crimes. I'm sure Gotham's got plenty of those. I loved the ending, I just wish they'd come up with some good reason for why Batman had to take a fall.
And as for Dent, I'm convinced he's still alive. First off, when moviemakers want you to know someone's dead, they usually show him lying there, eyes open. If they want to be maudlin about it, a good guy will come along and close the corpse's open eyes. Dent's good eye was closed, which said to me "unconscious." Second, they never said Dent died, and in sci fi and comics, if they don't explicitly say it (and sometimes even if they do), you can't count on it. Lastly, there was a lot of parallel structure (or repetition) in the movie. But two devices don't have a parallel unless you figure Dent's alive:
1. When Batman dangles him over a fire escape, Marone tells him he's got to learn that a fall from this height won't kill someone. The height of that fire escape seemed to me to be pretty similar to the distance Batman and Dent fell at the end, and the first thing I thought of was that scene with Marone.
2. They faked Gordon's death, and they did it convincingly. Why not also fake Dent's and lock him away in Arkham, hoping to eventually cure him?